Damages from sea level rise, as well as strategies to manage the associated risk, hinge critically on the time scale and eventual magnitude of sea level rise. Satellite observations and paleo-data suggest that the Greenland Ice Sheet (GIS) loses mass in response to increased temperatures, and may thus contribute substantially to sea level rise as anthropogenic climate change progresses. The time scale of GIS mass loss and sea level rise are deeply uncertain, and are often assumed to be constant. However, previous ice sheet modeling studies have shown that the time scale of GIS response likely decreases strongly with increasing temperature anomaly. Here, we map the relationship between temperature anomaly and the time scale of GIS response, by perturbing a calibrated, three-dimensional model of GIS behavior. Additional simulations with a profile, higher-order, ice sheet model yield time scales that are broadly consistent with those obtained using the three-dimensional model, and shed light on the feedbacks in the ice sheet system that cause the time scale shortening. Semi-empirical modeling studies that assume a constant time scale of sea level adjustment, and are calibrated to small preanthropogenic temperature and sea level changes, may underestimate future sea level rise. Our analysis suggests that the benefits of reducing greenhouse gas emissions, in terms of avoided sea level rise from the GIS, may be greatest if emissions reductions begin before large temperature increases have been realized. Reducing anthropogenic climate change may also allow more time for design and deployment of risk management strategies by slowing sea level contributions from the GIS.